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Solar Magnetic Fields
Capacitors in Circuits
 Charge takes time to
move through wire
 V is felt at the speed
of light, however
 Change in potential
across capacitor is
V = q / C
 Charge on capacitor is
time dependent
Section 19.5
Current and Capacitors
 No charge flows from one plate to the other in a
capacitor.
 There is a net current through a capacitor, though.
 Positive charge flows onto one plate
 Negative charge flows onto the other plate from the
opposite direction.
 Positive flow in one direction is the same as negative
flow in the other direction
RC Circuits
 When the switch is
open,
 No current flows (open
circuit), I = 0
 Voltage across resistor,
VR = I R = 0
 Voltage across capacitor,
VC = 0
 Charge on capacitor,
Q = C VC = 0
Section 19.5
RC Circuits, cont.
 Just after the switch is
closed, (t = 0)
 Charge takes time to move
so Q = 0
 VC = Q / C = 0
 VR =
ε
 Current in circuit, I = V / R
=ε/R
Section 19.5
RC Circuits, cont.
 After the switch is
closed for a long time,
(t = ∞)
 Charge builds up until
potential across capacitor
equals emf of battery,
VC = ε
 Q = C VC = C
ε
 VR = 0
 Current in circuit, I = 0
Section 19.5
Time Constant, τ = RC
 Current
 At the end of one time constant, the
current has decreased to 37% of its
original value
 At the end of two time constants, the
current has decreased to 14% of its
original value
 Voltage and charge
 At the end of one time constant, the
voltage and charge have increased to
63% of the original value.
Section 19.5
Electrostatics Summary
 Fields and Forces
 Coulomb’s Law
 Electric Flux and Gauss’s Law
 Conductors and Insulators
 Energy and Potential
 Conservation of energy
 Current and Circuits
 Drift velocity
 Capacitors, Resistors, and Batteries
 Kirchhoff’s Rules
 Series and Parallel
Section 19.5
Chapter 20
Magnetic Fields and Forces
Magnetic Levitation:
http://www.youtube.com/watch?v=m-Al7GAnH8Q
Bar Magnet
 A bar magnet is a
permanent magnet in the
shape of a bar
 The symbol for the
magnetic field is B
 The magnetic field lines
can be deduced from the
pattern of the iron filings
 The filings are small,
needle-shaped,
permanent magnets
Section 20.1
Magnetic Field Lines
 The magnetic poles are
indicated at the ends of
the bar magnet
 Called north and south
 The magnetic poles are
analogous to positive
and negative charges
 The north poles of the
filings are attracted to
the south pole of the bar
magnet
Section 20.1
Magnetic Field from Current
 Moving charges
produce magnetic fields
 An electric current
consists of moving
charges, so it will
produce a magnetic
field
 The iron filings show the
magnetic field pattern
due to the current
Section 20.1
Right-Hand Rule
 Point the thumb of your
right hand in the
direction of the current
 You thumb will be
parallel to the wire
 Curling the fingers of
your right hand around
the wire gives the
direction of the
magnetic field
Section 20.1
Plotting Field Lines
 Field lines are three-
dimensional
 A large dot (•) indicates
the tip of the vector
when it points out of the
plane
 A cross (×) denotes the
tails of the vector when
it points into the plane
Section 20.1
Charges and Magnetic Fields
 The electric current can be modeled as a collection
of positive electric charges
 The charges would be moving with a velocity parallel
to the current direction
 The direction of the magnetic field is given by the
right-hand rule
 A positive charge moving to the left produces the
same magnetic field as a negative charge moving to
the right
Section 20.1
Magnetic Field and Current
Loop
 Treat the loop as many
small pieces of wire
 Apply the right-hand
rule to find the field from
each piece of wire
 Applying superposition
gives the overall pattern
shown in fig. 20.9B
Section 20.1
Two Parallel Wires
1
I
 What is the direction of
the magnetic field in
regions 1, 2 and 3?
2
I
3
Two Parallel Wires
Magnetic Forces & Bar Magnets
 To determine the total
force on the bar
magnet, you must look
at the forces on each
pole
 The total force is zero
 The total torque is nonzero
 The torque acts to align
the bar magnet along
the magnetic field
Section 20.2
Magnetic Moment
 The bar magnet possesses a magnetic moment
 The bar magnet is similar to an electric dipole
 The poles of the magnet can be thought of as a sort of
“magnetic charge”
 The north pole of one magnet will attract the south
pole of another magnet
 Unlike poles attract
 Like poles will repel
 Similar to electric charges
Section 20.2
Comparing Electric and
Magnetic Fields and Forces
 There are many similarities in the behavior of electric
charges and magnetic poles
 Unlike charges and unlike poles attract
 Like charges and like poles repel
 North and south magnetic poles always occur in
pairs
 It is not possible to obtain an isolated magnetic pole
Section 20.2
Force on Moving Charge
 Magnetic force acts on individual charges
 The force depends on the velocity of the charge
 If the charge is not moving, there is no magnetic force
 If a positive charge, q, is moving with a given
velocity, v, in an external magnetic field, B, then the
magnitude of the force on the charge is
 FB = q v B sin θ
 The angle θ is the angle between the velocity and the
field
Section 20.3
Right Hand Rule 2
 To determine the
direction of the force,
use right hand rule 2
 Point the figures of your
right hand in the
direction of the velocity
and curl them in the
direction of the field
 Your thumb points in
the direction of the force
Section 20.3
Motion of a Charged Particle
 Assume a charged
particle moves parallel
to the magnetic field
 The angle between the
velocity and the field is
zero
 Therefore, the force is
also zero
 Since sin θ = 0
Section 20.3
Motion of a Charged Particle, 2
 Assume a charged
particle moves
perpendicular to the
magnetic field
 The angle between the
velocity and the field is
90o
 Therefore, the force is
qvB
 The particle will move in
a circle
Section 20.3
Motion, 2, cont.
 The circle lies in the plane perpendicular to the
magnetic field lines
 The radius of the circle can be calculated from noting
there must be a centripetal force acting on the
particle
FB  FC

mv 2
qvB 
r
mv
r 
qv
Section 20.3
Motion of a Charged Particle, 3
 Assume a charged
particle moves neither
parallel nor perpendicular
to the magnetic field
 The angle between the
velocity and the field
varies
 The path of the particle is
helical
 The charged particle will
spiral around the
magnetic field lines
Section 20.3
Example: Bubble Chamber
 Used in particle physics
to investigate decay
products
 What is the sign of the
charge?
 What is the relative
mass?
Right Hand Rules, Summary
 Right-hand rule number 1: Finding the direction of the
magnetic field from an electric current
 Place the thumb of your right hand along the direction of the
current
 Curl your fingers; they will then give the direction of the magnetic
field as the field lines encircle the current
 Right-hand rule number 2: Finding the direction of the
magnetic force on a moving charge, q
 Point the fingers of your right hand along the direction of the
velocity
 Curl your fingers in the direction of the field

Curl your fingers through the smallest angle that connects the velocity
and the field
 If q is positive, the magnetic force is parallel to your thumb. If q is
negative, the magnetic force is in the opposite direction
Section 20.3
Earth’s Magnetic Field
 The Earth acts like a
very large magnet
 A compass needle
aligns with its north
magnetic pole pointing
approximately toward
the Earth’s geographic
north pole
 So the Earth’s
geographic north pole
is actually a south
magnetic pole
Section 20.9
Earth’s Magnetic Field, cont.
 The location of the Earth’s south magnetic pole does
not correspond exactly with the geographic north
pole
 The Earth’s south magnetic pole moves slowly
 Currently at about 40 km/year
 The Earth’s magnetic field has completely reversed
direction
 The field is probably produced by electric currents in
the core
Section 20.9
Cosmic Rays
 Charged particles from




space are called cosmic
rays
Their motion is affected by
the Earth’s magnetic field
At the equator, the particles
are deflected away from the
Earth’s surface
At the poles, the particles
follow a helical path and
spiral into the poles
They interact with the
Earth’s atmosphere and
produce aurora
Section 20.9